Yes, microwaves pass perfectly through quartz. The only effect is a step in permittivity.
In the low-pressure gas, they induce a glow discharge. Similar to what electrodes would do, but from distance, through the induced electric field.
It avoids contamination of the gas by the electrodes bombarded with ions, needs no metal-to-glass seals, and more advantages.
"Ionizing" radiation is understood as high-energy particles. It's a matter of wording, but for sure, microwaves don't fit in this category. And in the discharge, electrons and ions ionize more molecules; the microwaves provide the accelerating field only.